Аннотация:
Let ${\mathcal S}'$ denote the set of all Schwartz distributions
and ${\mathcal P}$ the set of all polynomials.
If we define ${\mathcal S}_\infty$ to be the set of all $f \in {\mathcal S}$
such that
$\int_{{\mathbb R}^n}x^\alpha f(x)\,dx=0$
for all $\alpha$,
we can consider the dual space ${\mathcal S}_\infty'$.
We know that ${\mathcal S}_\infty'$ is isomorphic to ${\mathcal S}'/{\mathcal P}$ as
linear spaces. But it seems to me that this is true topologically.
In my Japanese book, I wrote a proof but I have commited the mistake.
But recently I modified the proof.
My result is as follows.
Theorem.
Equip ${\mathcal S}'$ and ${\mathcal S}'_\infty$ with the weak star topology.
Then the restriction mapping from ${\mathcal S}'$ to ${\mathcal S}_\infty'$ is open.
Язык доклада: английский
Список литературы
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S. Nakamura, T. Noi, Y. Sawano, “Generalized Morrey spaces and trace operator” (to appear)
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Y. Sawano, Theory of Besov Spaces, Nihon-Hyoronsha, 2011, 440 pp. (in Japanese)
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